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C7×C5⋊(D31⋊C9) #34086144

order19530
automorphism?
homologyAbelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×C5⋊(D31⋊C9)
unambiguous semidirect productC5⋊(C7×D31⋊C9)
unambiguous semidirect product(C31⋊C9)⋊(C7×D5)
unambiguous semidirect productD155⋊(C7×C9)

Splittings

derived, HallC5×C31 ⋊ C2×C7×C9
HallC5×C7×C31⋊C9 ⋊ C2
HallC7×D155 ⋊ C9
HallC7×C31⋊C9 ⋊ D5
HallC5×C31⋊C9 ⋊ C2×C7
HallC5×C7×C31 ⋊ C2×C9
HallD155 ⋊ C7×C9
HallC31⋊C9 ⋊ C7×D5
HallC7×C31 ⋊ C9×D5
HallC5×C7 ⋊ D31⋊C9
SylowC31 ⋊ C7×C9×D5
SylowC5 ⋊ C7×D31⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C7C5⋊(D31⋊C3)
commutator, hypocenterC5×C31C2×C7×C9
FrattiniC3C7×C5⋊(D31⋊C3)
Fitting, socleC3×C5×C7×C31C2×C3
prime radicalC3×C7×D155C3
cosocleC3×C5×C31C2×C3×C7
LCSG ▷ C5×C31
UCSC1 ◁ C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9765

Conjugacy classes & character table

777 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 49);